Mountain bikes are getting more and more popular for sport and leisure. To enable a mountain bike to meet the severe terrain of a mountain, the bike is equipped with a plurality of heavy-duty shock absorbers at different positions thereof. However, till now, there is no mountain climbing bike disclosed to be equipped with a shock absorber between a seat tube and a down tube thereof to absorb a shock possibly occurring on a connecting portion of the seat tube and the down tube wherein the connecting portion is also subjected to a large shocking force when the bike is ridden on the mountain.